Invariant parametrizations and complete systems of global invariants of curves in the pseudo-Euclidean geometry

Authors : Ömer PEKŞEN, Djavvat KHADJIEV, İdris ÖREN

Pages : 147-160

View : 13 | Download : 4

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let Minsert ignore into journalissuearticles values(n, p); be the group of all transformations of an n-dimensional pseudo-Euclidean space Enp of index p generated by all pseudo-orthogonal transformations and parallel translations of Enp. Definitions of a pseudo-Euclidean type of a curve, an invariant parametrization of a curve and an Minsert ignore into journalissuearticles values(n, p);-equivalence of curves are introduced. All possible invariant parametrizations of a curve with a fixed pseudo-Euclidean type are described. The problem of the Minsert ignore into journalissuearticles values(n, p);-equivalence of curves is reduced to that of paths. Global conditions of the Minsert ignore into journalissuearticles values(n, p);-equivalence of curves are given in terms of the pseudo-Euclidean type of a curve and the system of polynomial differential Minsert ignore into journalissuearticles values(n, p);-invariants of a curve xinsert ignore into journalissuearticles values(s);.
Keywords : Curve, pseudo Euclidean geometry, invariant parametrization